100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

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254 P. R. Saulsonplans to continue improving and to continue coordinated running. Soon,too, Virgo’s 3 km interferometer will come on line. It is expected have asensitivity comparable to LIGO’s. This set of detectors will constitute apowerful global network in the search for gravitational waves.In case we aren’t lucky enough to find signals at this level of sensitivity,there is a plan that ought to ensure success. The initial conception of LIGO(and the vision approved by the NSF) called for evolution in the installed interferometers.Almost since the start of the construction of LIGO, researchhas been moving forward on ways to build a better interferometer. One ofthe earliest and main roles of the LIGO Scientific Collaboration has beento coordinate this research and to pull it together into a coherent design.The outcome of that work was the proposal to build Advanced LIGO. 31Expected to improve sensitivity by at least a factor of ten at high frequenciesand to extend the observing band down as low as 10 Hz, AdvancedLIGO will use the same buildings and vacuum system as initial LIGO, butwill replace all of the interferometer components. At that new standard ofperformance, standard astronomical wisdom predicts that a multitude ofsignals will be within our grasp. (There are also plans for advanced interferometersunder serious consideration in Japan and in Europe.)Fig. 7. A model of the noise spectrum of the “reference design” for Advanced LIGO,compared with the SRD noise floor of initial LIGO. There are several features worthy ofnote. Seismic noise will not be important above 10 Hz. At most frequencies shown, thespectrum is dominated by fundamental interferometer sensing noise (shot noise at highfrequencies, radiation pressure noise at low frequencies. Thermal noise from the mirror’sinternal modes of vibration is important in the vicinity of 100 Hz.
Receiving Gravitational Waves 255In November 2004, the National Science Board approved AdvancedLIGO. It is hoped that funding will be approved by the U.S. Congresswithin a few years, so that Advanced LIGO can begin searching the skiesearly in the next decade.AcknowledgmentsThe author’s research is supported by National Science Foundation GrantPHY-0140335. The Laser Interferometer Gravitational Wave Observatoryis supported by the National Science Foundation under Cooperative AgreementPHY-0107417.References1. M. Bartusiak, Einstein’s Unfinished Symphony: Listening to the Sounds ofSpace-Time (Joseph Henry Press, Washington, D.C., 2000).2. H. Collins, Gravity’s Shadow: The Search for Gravitational Waves (Universityof Chicago Press, Chicago, 2004).3. P. R. Saulson, Fundamentals of Interferometric Gravitational Wave Detectors(World Scientific, Singapore, 1994).4. B. Barish and R. Weiss, Physics Today 52 no. 10, 44 (1999).5. A. Einstein, Sitzungsberichte, Preussische Akademie der Wissenschaften688 (1916); A. Einstein, Sitzungsberichte, Preussische Akademie der Wissenschaften154 (1918).6. Peter Bergmann, private communication 1993.7. H. Bondi, Nature 179, 1072 (1957). In this article, Bondi credits I. Robinsonwith independent discovery of this proof, and also cites discussions at theChapel Hill meeting on gravitation in 1957.8. J. Weber, General Relativity and Gravitational Waves (Interscience, NewYork, 1961).9. P. Kafka and L. Schnupp, Astron. Astrophys. 70, 97 (1978).10. F. A. E. Pirani, Acta Phys. Polon. 15, 389 (1956).11. G. E. Moss, L. R. Miller, and R. L. Forward, Appl. Opt. 10, 2495 (1971);R. L. Forward, Phys. Rev. D 17, 379 (1978).12. M. E. Gertsenshtein and V. I. Pustovoit, Sov. Phys. JETP 16, 433 (1962).13. R. Weiss, Quarterly Progress Report, MIT Research Lab of Electronics 105,54 (1972).14. L. L. Smarr, ed., Sources of Gravitational Radiation (Cambridge UniversityPress, Cambridge, 1979).15. P. G. Roll, R. Krotkov, and R. H. Dicke, Ann. Phys. (N. Y.) 26, 442 (1964).16. R. Schilling, L. Schnupp, W. Winkler, H. Billing, K. Maischberger, and A.Rüdiger, J. Phys. E: Sci. Instrum. 14, 65 (1981).17. R. W. P. Drever, in Gravitational Radiation, eds. N. Deruelle and T. Piran(North Holland, Amsterdam, 1983), p. 321.
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Published byWorld Scientific Publis
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viA. Ashtekarof space-time that eme
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viiiA. AshtekarGravitational waves
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xA. Ashtekarhappy, schizophrenic at
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xviContents9. Receiving Gravitation
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4 J. Stachel(2) the change over tim
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6 J. StachelFig. 2respectively. Fur
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8 J. Stachelof string theory, M-the
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10 J. StachelLogically, it would se
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12 J. Stachelupon by no (net) exter
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14 J. Stachelof the incompatibility
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16 J. Stachelis an important differ
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18 J. Stachelbetween physical conce
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20 J. Stachel10. Four-Dimensional F
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22 J. Stachelderivative of the metr
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24 J. Stachel(b) General relativity
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26 J. Stachelfour-dimensional analo
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28 J. Stachelply the lessons learne
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30 J. Stachelmanifold appropriate f
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32 J. Stachelwhich merely defines t
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34 J. Stacheldynamical process as a
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36 J. Stachel9. J. Stachel, Special
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Part IIEinstein’s UniverseRamific
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40 H. Nicolai• Higher dimensions
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42 H. Nicolaiadvance, and possibly
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44 H. NicolaiBianchi identities are
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46 H. NicolaiIt does not appear pos
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48 H. NicolaiThe other SL(2, R), of
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50 H. Nicolai3.1. BKL dynamics and
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52 H. Nicolaidegrees of freedom, th
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54 H. Nicolaiin the valley. The Ham
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56 H. NicolaiThe main feature of th
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58 H. Nicolai4. Basics of Kac Moody
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60 H. Nicolaifor indefinite A. It i
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62 H. NicolaiThe level l = 0 sector
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64 H. NicolaiConsequently, the repr
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66 H. Nicolaiwhere the abelian part
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68 H. Nicolaiconstant momenta Π yi
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70 H. Nicolaiσ-model side is suppo
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72 H. NicolaiReferences1. H.A. Buch
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74 H. Nicolai44. G. Neugebauer and
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CHAPTER 3THE NATURE OF SPACETIME SI
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78 A. D. Rendallspacetime to define
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80 A. D. RendallOne of the most imp
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82 A. D. Rendalltheorems was an elu
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84 A. D. Rendallsymmetric solution
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86 A. D. Rendallback into a curvatu
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88 A. D. Rendallspace and there are
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The Nature of Spacetime Singulariti
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CHAPTER 4BLACK HOLES - AN INTRODUCT
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Black Holes 95It follows that ˙v d
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Black Holes 973221100-1-1-2-200-5-3
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Black Holes 99calculation of the de
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Black Holes 101family of null geode
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Black Holes 105(3) Ω is positive o
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Black Holes 107In dimension 3 + 1 t
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Black Holes 109A fundamental theore
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Black Holes 111(4) The Kerr black h
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Black Holes 113˚g ab =˚g ab (x a
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Black Holes 115It is a folklore the
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Black Holes 117⃗x 4 = −⃗x 3
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Black Holes 119Work partially suppo
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Black Holes 121totically flat space
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Black Holes 12376. R.C. Myers and M
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The Physical Basis of Black Hole As
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Probing Space-Time Through Numerica
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CHAPTER 7UNDERSTANDING OUR UNIVERSE
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Understanding Our Universe: Current
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Page 221 and 222: Understanding Our Universe: Current
Page 223 and 224: CHAPTER 8WAS EINSTEIN RIGHT? TESTIN
Page 225 and 226: Was Einstein Right? 207We begin in
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Page 229 and 230: Was Einstein Right? 211On this 100t
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Page 235 and 236: Was Einstein Right? 217of VLBI data
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Page 241 and 242: Was Einstein Right? 223be measured
Page 243 and 244: Was Einstein Right? 22510. J. G. Wi
Page 245 and 246: Was Einstein Right? 22761. C. M. Wi
Page 247 and 248: Receiving Gravitational Waves 229th
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Page 257 and 258: Receiving Gravitational Waves 239th
Page 259 and 260: Receiving Gravitational Waves 241to
Page 261 and 262: Receiving Gravitational Waves 243In
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Page 265 and 266: Receiving Gravitational Waves 247a
Page 267 and 268: Receiving Gravitational Waves 249ab
Page 269 and 270: Receiving Gravitational Waves 251Fi
Page 271: Receiving Gravitational Waves 253Eq
Page 275 and 276: CHAPTER 10RELATIVITY IN THE GLOBAL
Page 277 and 278: Relativity in the Global Positionin
Page 309 and 310: Part IIIBeyond EinsteinUnifying Gen
Page 311 and 312: CHAPTER 11SPACETIME IN SEMICLASSICA
Page 313 and 314: Spacetime in Semiclassical Gravity
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Spacetime in Semiclassical Gravity
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CHAPTER 12SPACE TIME IN STRING THEO
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Space Time in String Theory 313limi
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Space Time in String Theory 315luti
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Space Time in String Theory 317In s
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Space Time in String Theory 319of t
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Space Time in String Theory 321an o
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Space Time in String Theory 323arbi
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Space Time in String Theory 325an e
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Space Time in String Theory 327in a
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Space Time in String Theory 329doma
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Space Time in String Theory 331a tu
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Space Time in String Theory 333bran
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Space Time in String Theory 335is a
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Space Time in String Theory 337thes
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Space Time in String Theory 339The
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Space Time in String Theory 341gene
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Space Time in String Theory 343are
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Space Time in String Theory 345tion
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Space Time in String Theory 34723.
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Space Time in String Theory 34955.
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Gravity, Geometry and the Quantum 3
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£¢¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡
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Loop Quantum Cosmology 383inflation
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Loop Quantum Cosmology 385gravitati
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Loop Quantum Cosmology 387Secondly,
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Loop Quantum Cosmology 389sically d
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Loop Quantum Cosmology 391states an
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Loop Quantum Cosmology 393represent
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Loop Quantum Cosmology 3954.2.1. Di
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Loop Quantum Cosmology 397question
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Loop Quantum Cosmology 399exist. Th
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Loop Quantum Cosmology 401in the ex
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Loop Quantum Cosmology 403λ max or
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Loop Quantum Cosmology 405This happ
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Loop Quantum Cosmology 407Loop quan
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Loop Quantum Cosmology 409to obtain
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Loop Quantum Cosmology 411familiar
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Loop Quantum Cosmology 41334. M. Bo
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CHAPTER 15CONSISTENT DISCRETE SPACE
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Consistent Discrete Space-Time 417v
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Consistent Discrete Space-Time 419I
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Consistent Discrete Space-Time 421a
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Consistent Discrete Space-Time 423F
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Consistent Discrete Space-Time 4250
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Consistent Discrete Space-Time 4272
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Consistent Discrete Space-Time 429i
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Consistent Discrete Space-Time 431a
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Consistent Discrete Space-Time 433n
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Consistent Discrete Space-Time 435t
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Consistent Discrete Space-Time 437w
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Consistent Discrete Space-Time 439f
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Consistent Discrete Space-Time 441(
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Consistent Discrete Space-Time 443R
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CHAPTER 16CAUSAL SETS ANDTHE DEEP S
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Causal Sets and the Deep Structure
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CHAPTER 17THE TWISTOR APPROACH TOSP
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The Twistor Approach to Space-Time
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INDEXσ models, 57, 65, 693+1 formu
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Index 509inflation, 383, 385-387, 4
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